For coupling the fluid and solid systems, any suitable FSI coupling strategy can be employed. For this particular work, the immersed boundary (IB) method [1]} is used to couple the LB method of the fluid with the 3D FEM (or 3D-axisymmetric FDM) of the solid [2]}, [3]}.
This method has been extensively used to simulate FSI problems in cardiovascular biomechanics [4]}, [5]}, [6]}, [7]}. The body force term \(\mathbf {b}(x,t)\)  in Equation (REF ) is used as an interaction force between the fluid and the boundary in order to enforce the no-slip velocity boundary condition at the FSI interface. The Lagrangian force between the fluid and structure, \(\mathbf {B}(\mathbf {s},t)\) , is then calculated by a penalty scheme [1]} using the expression given by
\(B(\mathbf {s},t)=\alpha \left(\int ^t_0\left(V_f(\mathbf {s},t^\prime )-V_s(\mathbf {s},t^\prime )\right)\mathrm {d}t^\prime \right) +\beta \left(V_f(\mathbf {s},t)-V_s(\mathbf {s},t)\right),\) 
